TY - JOUR
T1 - Global weak solutions for an incompressible charged fluid with multi-scale couplings
T2 - Initial-boundary-value problem
AU - Jerome, Joseph W.
AU - Sacco, Riccardo
N1 - Funding Information:
The first author was supported by ONR/Darpa grant nr. LLCN00014-05-C-0241 and the second author was supported by the M.U.R.S.T. grant nr. 2006013187-003.
PY - 2009/12/15
Y1 - 2009/12/15
N2 - The Cauchy problem for the Poisson-Nernst-Planck/Navier-Stokes model was investigated by the first author in [J.W. Jerome, An analytical approach to charge transport in a moving medium, Transport Theory Statist. Phys. 31 (2002) 333-366], where a local existence-uniqueness theory was demonstrated, based upon Kato's framework for examining evolution equations. In this article, the existence of a global weak solution is proved to hold for the model, in the case of initial-boundary-value problem. Connection of the above analysis to significant applications is addressed, including bio-hybrid devices in neuronal cell monitoring, bio-reactor devices in tissue engineering and microfluidic devices in Lab-On-Chip technology.
AB - The Cauchy problem for the Poisson-Nernst-Planck/Navier-Stokes model was investigated by the first author in [J.W. Jerome, An analytical approach to charge transport in a moving medium, Transport Theory Statist. Phys. 31 (2002) 333-366], where a local existence-uniqueness theory was demonstrated, based upon Kato's framework for examining evolution equations. In this article, the existence of a global weak solution is proved to hold for the model, in the case of initial-boundary-value problem. Connection of the above analysis to significant applications is addressed, including bio-hybrid devices in neuronal cell monitoring, bio-reactor devices in tissue engineering and microfluidic devices in Lab-On-Chip technology.
KW - Initial-boundary problem for hybrid systems
KW - Navier-Stokes
KW - Poisson-Nernst-Planck
KW - Rothe's method
KW - Slip boundary condition
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U2 - 10.1016/j.na.2009.05.047
DO - 10.1016/j.na.2009.05.047
M3 - Article
AN - SCOPUS:72149102698
SN - 0362-546X
VL - 71
SP - e2487-e2497
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
IS - 12
ER -